JACKSON SCHOOL DISTRICT
Mathematics
COURSE PROFICIENCIES
Algebra 1B Part 1 and Part 2
Grade 9
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Description of Course Content
Algebra 1B is a two-semester course designed to meet the needs of students who have successfully completed 8th grade. The purpose of this course is to provide each student with the basic concepts associated with Algebra 1 and a variety of activities to practice those concepts. To meet the wide range of student learning styles and to encourage active involvement, strategies will vary. This course will provide students with a foundation for future math courses.
Description of Expected Learnings
I. Number and Numerical Operations
The student will:
A. Number Sense
1. Understand real numbers, powers, roots, exponents, absolute value,
scientific notation, properties of arithmetic operations, primes, factors,
and multiples.
2. Extend the understanding of the real number system to include
rational and irrational numbers.
a. Represent equivalent forms of the same number
b. Evaluate expressions containing powers, roots, and factorials
3. Understand equivalent and nonequivalent fractions, ratios, proportions, and percents.
4. Solve a variety of problems using proportions and percents.
5. Change from a fraction or decimal to a percent and from a percent to a fraction or decimal.
6. Compare effects of percent increase and percent decrease in price of objects where sales tax is applicable.
B. Numerical Operations
1. Extend understanding and use of operations to real numbers and algebraic procedures.
2. Develop, apply, and explain methods for solving problems involving rational and negative exponents.
3. Perform addition and subtraction with matrices.
4. Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.
C. Estimation
1. Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.
II.Geometry and Measurement
The student will:
A. Geometric Properties
1. Understand geometric terms.
2. Understand and recognize fundamental relationships between geometric figures.
a. Distinguish between parallel and perpendicular lines
b. Find the point of intersection of two lines
3. Apply concepts of symmetry, similarity, and congruence to problem solving.
B. Coordinate Geometry
1. Use coordinate geometry to represent and verify properties of lines.
a. Distance between two points
b. Midpoint and slope of a line segment
c. Slopes of parallel and perpendicular lines
2. Relate corresponding sides of similar figures.
3. Understand the rectangular coordinate system and use coordinates, maps, tables, matrices, and grids to solve real-world problems.
C. Units of Measurement
1. Develop and apply a variety of strategies for determining perimeter, circumference, area, surface area, volume, and angle measure.
2. Use standard and non-standard units of measure.
3. Understand dimensions, shapes, and properties of figures and objects.
4. Utilize appropriate formulas and label answers with appropriate units of measure.
D. Measuring Geometric Objects
1. Solve problems using the Pythagorean Theorem.
2. Use basic trigonometric ratios to solve problems involving indirect measurement.
III.Patterns and Algebra
The student will:
A. Patterns
1. Develop and use algorithms and flow charts to perform a given task.
2. Analyze and describe sequences, series, patterns, and limits found in the real world.
3. Use tables, rules, variables, open sentences and graphs to describe patterns and other relationships.
4. Construct, recognize, and extend patterns.
5. Use tables and graphs to identify patterns and relationships.
6. Use appropriate graphing techniques to represent patterns and real-world phenomena.
B. Functions and Relationships
1. Use relations and functions to solve problems arising from mathematical situations, everyday experiences, and other disciplines.
2. Understand relations, functions, independent and dependent variables, domain and range, and the rectangular coordinate system.
a. Find the slope of a line
3. Use linear and nonlinear functions to model mathematical situations and real-world phenomena.
4. Differentiate between graphing technologies to represent functions and real-world phenomena.
5. Analyze and represent functional relationships to explain how a change in one quantity results in a change in another quantity.
6. Express change in related quantities as a linear, quadratic, or periodic relationship in order to predict relations between quantities that change over time.
7. Recognize that real-world phenomena can be modeled using simple polynomial, rational, trigonometric, and exponential functions.
C. Modeling
1. Understand variables, expressions, number sentences, and open sentences.
2. Use linear equations and inequalities to model real-life situations.
3. Interpret algebraic equations and inequalities geometrically, and describe geometric objects algebraically.
4. Apply algebraic and fundamental mathematical models to problems arising from mathematical situations and everyday experiences.
D. Procedures
1. Perform algebraic order of operations.
2. Evaluate algebraic expressions.
3. Solve equations and inequalities using a variety of methods.
a. Paper-and-pencil techniques
b. Tables and graphs
c. Graphing calculators
4. Develop, explain, use, and analyze operations and algebraic procedures on real numbers and algebraic expressions.
5. Use algebraic methods to solve problems arising from mathematical situations, everyday experiences, and other disciplines.
IV. Data Analysis, Probability and Discrete Mathematics
The student will:
A. Data Analysis
1. Make predictions from data.
a. Scatter plot
b. Correlation techniques
2. Select an appropriate measure of central tendency or other statistical measure to describe data.
a. Mean, median, and mode
b. Range
3. Collect and organize an appropriate data display to make predictions.
a. Histograms
b. Bar graphs
c. Line graphs and plots
d. Matrices
e. Tables, lists, and charts
4. Use addition of matrices to manipulate data.
5. Make inferences and evaluate arguments based on an analysis of data.
B. Probability
1. Find theoretical and experimental probabilities.
2. Recognize probabilities as ratios and percents.
3. Find probabilities of simple and compound events.
a. Dependent
b. Independent
c. Equally likely
C. Discrete Mathematics – Systematic Listing and Counting
1. Use various methods to arrange, organize, analyze, store, transform and communicate information.
Evaluative Means to Determine Mastery
1. Teacher-prepared tests and quizzes.
2. Alternative assessments and homework assignments.
3. Final examinations.
4. Class participation.
5. Open-ended questions.
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10/25/04